My question involves paternity law for the State of: Alaska

I am 22 years old and currently have a child who is 9 months old and am soon to be married. I was in a previous relationship with someone who got pregnant a few weeks after we had gotten together. during our relationship, it was pretty rocky and was pretty much called a "sperm donor" and all i was to be used for child support. She had cheated on me three times and even hit me busting my lip. Towards the end of our relationship(about four months into the pregnancy) she had kicked me out several times, where i spent the majority of our relationship at a homeless shelter. I moved to tennessee where my family was closer for my own health. The ex had stayed in contact via email and internet. she told me that she was planning on having her current boyfriend(husband) sign the Birth Certificate as the Biological Father. I told her that if the child WAS mine that she shouldnt do that and to set up for a praternity test as i did not know the childs name nor any information regarding. She ended up having her husband sign the papers and stopped talking to me for almost two years. Now that I have a family of my own and I am trying to feed my family now, we have moved to michigan and assumed that the ex had taken care of everything "her" way. My mom had received a knock on the door from tennessee police stating that i have to take a paternity test and that since i was not in the state, that if i did not contact them that she would be jailed for aiding and abetting. What i want to know, is what im supposed to do, and what legal action a can take. If the child is mine, i dont want to have that child be with her mother as her mother already has a record for Child neglect(locked her first child in the bathroom for 6 hours to go party) and domestic violence. At the same time, i dont really want to look forward to child support because i know that the ex will end up using it for herself, the reason i say this is because she does not have full custody of her first child, and being that she is abusive. I'm just in a bind and being as how i'm not very knowledgeable about these situations, i could use the advice on what my options are. Thank You.